Solution: The GCF of 75 and 16 is 1
Methods
How to find the GCF of 75 and 16 using Prime Factorization
One way to find the GCF of 75 and 16 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 75?
What are the Factors of 16?
Here is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
And this is the prime factorization of 16:
2
4
2^4
2 4
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 75 and 16 is 1.
Thus, the GCF of 75 and 16 is: 1
How to Find the GCF of 75 and 16 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 75 and 16 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 75 and 16:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 16: 1, 2, 4, 8, 16
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 75 and 16 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 112 and 89?
What is the GCF of 104 and 12?
What is the GCF of 103 and 60?
What is the GCF of 71 and 78?
What is the GCF of 150 and 9?